Global solutions and finite time blow-up for fourth order nonlinear damped wave equation. (English) Zbl 1395.35137
Summary: In this paper, we study the initial boundary value problem and global well-posedness for a class of fourth order wave equations with a nonlinear damping term and a nonlinear source term, which was introduced to describe the dynamics of a suspension bridge. The global existence, decay estimate, and blow-up of solution at both subcritical (\(E(0) < d\)) and critical (\(E(0) = d\)) initial energy levels are obtained. Moreover, we prove the blow-up in finite time of solution at the supercritical initial energy level (\(E(0) > 0\)).{
©2018 American Institute of Physics}
©2018 American Institute of Physics}
MSC:
| 35L35 | Initial-boundary value problems for higher-order hyperbolic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35B44 | Blow-up in context of PDEs |
| 35P20 | Asymptotic distributions of eigenvalues in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
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